The Effect of the Random Magnetic Field Component on the Parker Instability

The Parker instability is considered to play important roles in the evolution of the interstellar medium. Most studies on the development of the instability so far have been based on an initial equilibrium system with a uniform magnetic field. However, the Galactic magnetic field possesses a random component in addition to the mean uniform component, with comparable strength of the two components. Parker and Jokipii have recently suggested that the random component can suppress the growth of small wavelength perturbations. Here, we extend their analysis by including gas pressure which was ignored in their work, and study the stabilizing effect of the random component in the interstellar gas with finite pressure. Following Parker and Jokipii, the magnetic field is modeled as a mean azimuthal component, $B(z)$, plus a random radial component, $\epsilon(z) B(z)$, where $\epsilon(z)$ is a random function of height from the equatorial plane. We show that for the observationally suggested values of $<\epsilon^2>^{1/2}$, the tension due to the random component becomes important, so that the growth of the instability is either significantly reduced or completely suppressed. When the instability still works, the radial wavenumber of the most unstable mode is found to be zero. That is, the instability is reduced to be effectively two-dimensional. We discuss briefly the implications of our finding.